pz := cos(t)^2;
py := -cos(t)^3*sin(t);
tz := -1/36*cos(t)*(-3+4*cos(t)^2)*(3*sin(2*t)+4);
ty := 1/18*sin(t)*(3*sin(2*t)+4);
tx := simplify(sqrt(tz^2+ty^2));

plot3d([tx*sin(s),py+ty*cos(s),pz+tz*cos(s)],
       t=0..Pi, s=0..2*Pi,
       grid=[99,25], style=patch, orientation=[170,120],
       scaling=constrained, lightmodel=light4);


# Here's a view with a slice cut out of it where it intersects itself:

plot3d([tx*sin(s),py+ty*cos(s),pz+tz*cos(s)],
        t=(Pi*.355)..(Pi*1.32), s=0..2*Pi,
        grid=[99,25], style=patch, orientation=[210,100],
        scaling=constrained, lightmodel=light4);